# Categorical resolutions of singularities (Kuznetsov)

I will discuss an approach to resolution of singularities of schemes

via derived categories of coherent sheaves. I will define what a categorical resolution

of singularities is, and will describe a construction of a categorical resolution

for any separable scheme of finite type over a field of characteristic zero (thus showing

that categorically any such singularity behaves as a rational singularity). Then I will

discuss the question of constructing small categorical resolutions, concentrating

on the notions of crepancy and explicit examples.